“The Prime Minister’s resignation has triggered a Tory leadership crisis. At the very time we need politicians to come together for the common good, the Tory party is plunging into a period of argument and infighting. In the absence of a government that puts the people first Labour must unite as a source of national stability and unity.

“It should focus on speaking up for jobs and workers’ rights under threat, and on challenging any attempt to use the referendum result to introduce a more right-wing Tory government by the backdoor.

“The last thing Labour needs is a manufactured leadership row of its own in the midst of this crisis and we call upon all Labour MPs not to engage in any such indulgence.”

Writing the The Guardian, Unite general secretary Len McCluskey said: “Those Labour MPs plunging their party into an unwanted crisis are betraying not only the party itself but also our national interest at one of the most critical moments any of us can recall.

“Hilary Benn and others have decided this is the moment to let the Tories off the hook and turn Labour inwards and try to set aside the overwhelming result of a party leadership election held less than 10 months ago.

“It seems clear that this coup would have been launched irrespective of the referendum result. Anyone who thinks remain would have won the vote if Jeremy Corbyn had told traditional Labour areas that all was well with the EU and with globalisation is living in a dream world. It is easier to do that from an oligarch’s yacht or a bank boardroom than it is in our de-industrialised cities and towns.

“A new leadership election is divisive and unnecessary. But if enough MPs want one, then bring it on. I am sure that Corbyn will secure a fresh mandate. But let me make two things clear.

“First, if anyone is undemocratic enough to think that there can be a new leadership election with the existing leader kept off the ballot, then they are setting the Labour party on course for a split.

“And second, Unite has hitherto opposed any plans to change the party rules governing mandatory re-selection of Labour MPs. That, too, we have looked on as a divisive distraction.

“But those MPs who have missed no opportunity to tweet and brief against the party’s elected leader over the last 10 months will find that their disloyalty finds no favour with party members and will make this an increasingly difficult line to hold.”

FBU general secretary Matt Wrack said: “Trade unionists and Labour Party members will be baffled and angry about these resignations that appear to have been coordinated to cause maximum damage. It is bizarre that some of the MPs making the loudest criticism of Jeremy Corbyn over the referendum completely failed to convince the electorate in their own constituencies.

“Following the referendum, Labour should be setting out policies to defend jobs, public services and wages as an exit from the EU is negotiated. Instead, some Labour MPs are playing irresponsible and silly games from their Westminster bubble. They should respect the overwhelming democratic mandate which Jeremy Corbyn achieved only last September.”

BFAWU President Ian Hodson tweeted: “The Labour Party is the members and we will fight to keep it.”

RMT general secretary Mick Cash said: “By peddling the ludicrous notion that Jeremy is somehow responsible for the EU referendum result, Jeremy’s critics are in fact insulting the intelligence of voters and in doing so further alienating millions of natural Labour supporters who are quote capable of making their own minds and who voted for what they believed in.

“After a divisive referendum, and with the Tories on the ropes, working class people want the Labour Party to unite and address their concerns, instead those attacking Jeremy risk plunging the party into civil war and handing a gift to the Tories.

“Jeremy has renewed the faith that many rank and file trade unionists have in the Labour Party which is vital in helping Labour assist in maintaining and increasing support amongst its base. Trying to force him from office will weaken, not strengthen the Labour Party.”

CWU general secretary Dave Ward said: “Jeremy Corbyn is and remains the catalyst for change in the Labour Party and the country. He has our full support. Those who seek to oust him represent the politics that forgot ordinary people.”